RISK AND RETURN
Beheler, Brown, Gonzalez, Moore, Siegert,
Tansey, & Wyatt
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Overview
• Expected and Realized Rate of Return
• Stand-Alone Risk and Return
• Portfolio Risk and Return
• The Calculation of Beta
• The Relationship Between Risk and Return
• Overarching Theme: To increase the rate of monetary
gain, you have to assume more risk
• Make educated investment decision and don’t follow
blindly.
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EXPECTED AND
REALIZED RATES OF
RETURN
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Expected and Realized Rates of Return
• “a bird in the hand is worth two in the bush”
• Is two birds in the bush valued higher than one?
• This expression means that it is better to have an
advantage or opportunity that is certain than having one
that is worth more but is not so certain.
~urbandictionary.com
• It is central theme of financial risk and uncertainty
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Expected Rate of Return
• Expected rate of return = ∑i = 1n [P(i) × ri]
• Expected return- The weighted average of the return
distribution where the weights are probability of
occurrences.
• Simple definition: The likelihood of possible outcomes of a
financial decision equaling a theoretical model of your
return on an investment.
• Say you want to invest into a stock. The stock may do well
or poorly. This formula gives you an average of how well
or poorly you will do.
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Expected Rates of Return
• Example: you got a fat check from Grandma for your
birthday and you want invest in Apple Inc. The current
price of the stock is $100. You know that the iPhone 6 is
coming out and you think it might impact the stock price.
• Let’s look at the following possible scenarios
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Expected Rates of Return
3 Scenarios:
A.
The iPhone 6 is freaking amazing and Siri becomes your personal assistant, doing everything for you.
The phone is actually a transformer and can turn into a microwave, cute robot dog, and a Segway.
Signaling awesomeness and netting you a 25% rate of return.
B.
The new iPhone is cool and most people want it, thus more people are buying it and the stock
moderately increases signaling moderate growth, but no Segway. 12% rate of return
C.
The new iPhone blows- all they did was wrap the screen along the side (making it more breakable than
the stemware you never use). The only other advancement was that they move the 8mm headphone
jack to the back center of the phone…why? Also the watch fails, because people realize they look like
idiots talking to it and will never be as cool as Dick Tracy. You will lose money. -5% rate of return.
• The probability of these scenarios happening:
• Scenario A: awesomeness: 30%
• Scenario B: average: 50%
• Scenario C: Epic fail: 20%
To find the expected rate of return, simply multiply the percentages by their
respective probabilities and add the results: = ∑i = 1n [P(i) × ri]
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Expected Rates of Return
• REMINDER: The probability of these scenarios happening:
• Scenario A: awesomeness: 30% @ 25% return
• Scenario B: average: 50% @ 12% return
• Scenario C: Epic fail: 20% @ -5% return
• To find the expected rate of return, simply multiply the percentages by their
respective probabilities and add the results:
Probability
Rate of Return
Total
30%
25%
7.5%
50%
12%
6%
20%
-5 %
-1%
Average potential gain or expected rate of return
12.5%
• (30% × 25%) + (50% × 12%) + (20% × –5%) = 7.5%+ 6 %–1%= 12.5%
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Realized Rates of Return
• The realized rate of return is simply what you actually get from the
investment.
• For example, the day Apple released the new iPhone, it did not
transform, but did have moderate success. And the stock price
increased 10%. This is the realized rate of return.
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Expected and Realized Rates of Return
IMPORTANT POINTS
• The probability totals must always equal 100%
for the calculation to be valid.
• Be sure not to overlook any negative numbers
in the calculations, or the results produced will
be incorrect.
• An E(R) calculation is only as good as the
scenarios considered. Unrealistic scenarios will
produce an equally unreliable expected rate of
return.
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STAND-ALONE RISK
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Stand-Alone Risk
• Stand-alone risk indicates the tightness of an investment
return distribution. Hopefully, this triggers a Quant1
flashback to standard deviation (SD or that Greek thing σ).
• Considers an investment or project in isolation.
• A financial calculator will likely not have functions needed
for these problems.
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Stand-Alone Risk
• The math to calculate Variance
• (Probability of Return 1 x [Rate of Return 1 – E(R)]2) + (Probability
of Return 2 x [Rate of Return 2 – E(R)]2) and so on
• Standard deviation= square root of variance
• Now let’s calculate the variance and σ for two
independent investment options.
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Stand-Alone Risk
Scenarios for growth of Southwest Airlines
Scenario
Probability
Rate of Return
Very Good
20%
12%
Good
25%
10%
More than a Saving Account
30%
8%
Poor
15%
5%
Fail
10%
-5%
Expected Rate of Return
Total
STEP 1: Find the totals for each row
STEP 2: Add the column for the grand total- this is the E(R)
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Stand-Alone Risk
Scenarios for growth of Southwest Airlines
Scenario
Probability
Rate or Return
Very Good
20%
12%
Good
25%
10%
More than a Saving Account
30%
8%
Poor
15%
5%
Fail
10%
-5%
Expected Rate of Return
•
Total
2.4%
2.5%
2.4%
0.8%
-0.5%
7.6%
Variance= (Probability of Return1 x [Rate of Return1 – E(R)]2) +…
• (0.20 x [12%-7.6%]2) + (0.25 x [10%-7.6%]2) + (0.30 x [8%7.6%]2) + (0.15 x [5%-7.6%]2) + (0.10 x [-5%-7.6%]2) = 22.25
• σ = √22.25 = 4.72
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Stand-Alone Risk
Scenarios for growth of JetBlue
Scenario
Probability
Rate of Return
Very Good
20%
18%
Good
30%
12%
More than a Saving Account
35%
5%
Poor
10%
-4%
Fail
5%
-20%
Expected Rate of Return
Total
• Find the Stand-Alone Risk for JetBlue, with numbers as
shown above
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Stand-Alone Risk
Scenarios for growth of JetBlue
Scenario
Probability
Rate of Return
Very Good
20%
18%
Good
30%
12%
More than a Saving Account
35%
5%
Poor
10%
-4%
Fail
5%
-20%
Expected Rate of Return
Total
3.6%
3.6%
1.8%
-0.4%
-1.0%
7.6%
• Variance= (0.20 x [18%-7.6%]2) + (0.30 x [12%-7.6%]2) +
(0.35 x [5%-7.6%]2) + (0.10 x [-4%-7.6%]2) + (0.05 x [20%-7.6%]2) = 81.36
• σ = √81.36 = 9.02
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Stand-Alone Risk
• What does a comparison of Southwest’s and JetBlue’s
standard deviation tell us?
Southwest σ
= 4.72
JetBlue σ
= 9.02
• Would the amount invested alter the stand-alone risk?
• What would the relative size of an investment alter?
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Coefficient of Variation (CV)
• In scenarios where the E(R) differ substantially, Standard
deviation alone may not be the best indicator.
• Coefficient of Variance measures the risk per unit of
return.
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Coefficient of Variation (CV)
σ / E(R)= CV
• Southwest
• Jet Blue
= 4.72/ 7.55 = 0.63
= 9.02/7.55 = 1.19
• A higher coefficient means there is more risk
• According to Standard Deviation and Coefficient of
Variance, Jet Blue is of higher risk.
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LET’S PRACTICE!
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Summary of Excel Computations
• Excel + YouTube=your mind blown …and summarize the
topic.
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PORTFOLIO RISK AND
RETURN
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Stand-Alone vs. Portfolio
• What is the difference between a stand-alone
stock and a stock in a portfolio?
• Rate of return- not on individual investment but rather
on the entire portfolio
• Riskiness of investment- focuses only on the entire
portfolio
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What are Portfolios?
• Portfolio- a number of individual investments held
collectively
• What are portfolios made up of?
• Individuals: Securities (i.e., stocks and bonds)
• Businesses: Projects (i.e., products or service lines)
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What are Portfolio Returns?
• A portfolio’s return is simply the weighted average
of the returns of the components
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Calculating Expected Rate of Return
E(Rp)= (w1 x E[R1])+(w2 x E[R2]) +(w3 x E[R3])
and so on
• w1 is the proportion of Investment 1 in the overall
portfolio
• E[R1] is the expected rate of return on Investment 1
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Example
• Find the Expected Rate of Return for a portfolio with an
equal weighted portfolio (50/50) of Ray Rice Chex and
Southwest Airlines stocks with the following data:
Expected Rate of Return
Ray Rice Chex
Southwest Airlines
-0.1%
7.6%
E(Rp)= (w1 x E[R1])+(w2 x E[R2])
E(Rp)= (50% x -0.1%)+(50% x 7.6%)= 3.75%
Weight of Ray Rice
Chex
Expected Ray Rice
Chex Rate of Return
Weight of Southwest
Airlines
Expected Southwest
Airlines Rate of Return
What happens if the weights change to Ray Rice Chex 40% and
Southwest Airlines 60%?
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What is Portfolio Risk?
• A portfolio’s risk typically is measured by its
standard deviation
• This is not merely the weighted average of each
component’s standard deviation.
• It depends on the relationships among the returns.
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Portfolio Risk: Two Investments
• Flip a coin once:
• $10,000 for Heads
• ($8,000) for Tails
• Expected $ return (0.5 x $10,000) + (0.5 x -$8,000)=
$1,000
• Would you take this bet?
• Suppose you could do it 100 times but $100 for Heads
and -$80 for Tails
• How does the risk differ? Which bet would you prefer?
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Diversifiable Risk vs. Portfolio Risk
• Market Portfolio- a portfolio containing all publicly
traded stocks.
• Don’t need to own large number of stocks to gain
risk-reducing benefits
• Well-diversified portfolio of about 50 randomly selected
stocks
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Diversifiable Risk vs. Portfolio Risk
• Diversifiable Risk
• Risk that can be
eliminated by
diversification
• Portfolio Risk
• The risk that is left over
after diversification
Stand-Alone risk= Diversifiable risk +
Portfolio risk
How does this work in healthcare?
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Portfolio Risk: Many Investments
• Most companies or
individuals are not
restricted to just twosecurity portfolios.
• Why can the risk
never reach zero?
•
All investments are
affected to a lesser or
greater degree by
general economic
conditions.
•
It is the positive
correlation among realworld investment
returns that prevents
investors from creating
riskless portfolios.
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Implications for Investors
• Holding a single investment is not rational
• Investors that are risk averse should seek to
eliminate all diversifiable risk
• Healthcare businesses that offer a diverse line of
services are less risky than ones with only a
single service
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Correlation Coefficient
• Correlation is the movement relationship of two variables.
• What measures this relationship?
• Correlation Coefficient = r
• Three kinds of correlations:
• Perfectly Negative: r = -1.0
• Negative values indicate a relationship between the two variables in that
as the 1st variable increases the 2nd variable decreases
• Perfectly Positive: r = 1.0
• Positive values indicate that if one variable increases, the other variable
increases as well and vice versa
• Uncorrelated: r = 0
• No relationship between values
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THE CALCULATION OF
β (BETA)
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β (beta) Coefficient
• Common measure of risk
• A measure of the volatility of investment returns relative to
the return on the portfolio.
• Shows the tendency of a portfolio’s returns to respond to
swings in the market.
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β Coefficient Values
• β = 1: investment’s price will move with the market; has
AVERAGE RISK
• β < 1: investment is less volatile than market; has LOW
RISK
• β > 1: investment is more volatile than market; has HIGH
RISK
• Most investments’ β are between 0.5 and 1.5
• http://www.investopedia.com/video/play/understanding-
beta/
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β
• Staple stocks relatively unaffected by the market cycle
have lower β :
• Wal-Mart Stores β = 0.31
• Tech stocks tend to be more volatile and have higher β :
• Google β = 1.45
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β Calculation
• β = (σi/σM) X (ri,M)
σi = standard deviation of investment returns
σM = standard deviation of the market returns
ri,M = correlation coefficient between investment and market
----OR----
• β = Covariancei,M / VarianceM
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β Usefulness
• The β is a useful tool for investors
• Used to compare historical data to measure riskiness of
investments
• Cannot predict future market changes
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Walk-through Exercise
• Extract historical prices for stock and index
• Calculate returns for both the stock and index
• Calculate β using regression formula and slope formula
• Graphically illustrate the relationship between the stock
and the index
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Practical Exercise 1
• Extract historical prices for Aflac and S&P 500 index for
the period from 15 September 2011 to 15 September
2014
• Calculate returns for both the stock and index
• Calculate β using regression formula and slope
formula
• Graphically illustrate the relationship between the stock
and the index
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Practical Exercise 2
• Extract historical prices for Johnson & Johnson and S&P
500 index for the period from 18 September 2012 to 18
September 2014
• Calculate returns for both the stock and index
• Calculate β using regression formula and slope
formula
• Graphically illustrate the relationship between the stock
and the index
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THE RELATIONSHIP
BETWEEN RISK AND
RETURN
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Risk & Required Return
Basic question:
How much return is required to
compensate investors for assuming a
given level of risk?
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The Capital Asset Pricing Model (CAPM)
• Model that
demonstrates the
relationship between
the market risk of a
stock, as measured
by its market beta,
and its required rate
of return
• CAPM relationship
between risk and
required rate of return is
given by Security
Market Line (SML)
equation
 R(Re) = RF + (R[Rm] – RF)
xβ
 R(Re) = RF + (RPm x β)
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SML Example
• Example: GeneralHealth stock
 RF = 6%
 R(Rm) = 12%
 β = 0.8
 QUESTION: If the E(RGH) = 15%, should investors buy/sell?
• REMEMBER THE FORMULA: R(Re) = RF + (R[Rm] – RF) x β
• Plug-in the example values
•
•
•
•
R(Re) = 6% + (12% – 6%) x 0.8
R(Re) = 6% + (6% x 0.8)
R(Re) = 10.8%
Answer: Buy because E(R) > R(R)
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SML Example Continued
• Same stock with different β would have different
required rate of return [R(Re)]
Recall: original example R(Rβ=0.8) = 10.8%
 R(Rβ=1.5)= 6% + (6% x 1.5) = 15%
 Riskier than original (β of 1.5 > 0.8)
 R(Rβ=1.0)= 6% + (6% x 1.0)= 12%
 Same as market return [R(Rm)] where β=1
 R(Rβ=0.5)= 6% + (6% x 0.5)= 9%
 Below-average risk (β<1.0)
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Graphic Representation
Required Rate of
Return (%)
15
12
9
6
0.5
1.0
1.5
Risk (β)
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SML Example Continued
Recall: Average risk stock had R(Rm)= 12% & RF = 6%
• RPm depends on the degree of aversion that investors in
the aggregate have to risk
 In average risk example, RPm = (12% - 6%)= 6%
 If degree of risk aversion increased, might increase to 14%; so,
now RPm = (14% - 6%)= 8%
 THE GREATER THEN DEGREE OF RISK AVERSION IN THE
ECONOMY, THE HIGHER THE REQUIRED RATE ON THE MARKET &
THE HIGHER THE REQUIRED RATES OF RETURN ON ALL STOCKS
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CAPM
• Advantages
• Simple & logical
• Focuses on the impact a
single investment has on a
portfolio
• Tells that the R(R) is
composed of a risk-free
rate, which compensates
investors for time value + a
risk premium that is a
function of investors’
attitudes towards risk
bearing in the aggregate
and the specific portfolio
risk of the investment
being evaluated
• Disadvantages
• Based on a very restrictive
set of assumptions that
does not conform well to
real-world conditions
• Theory based on
expectations while only
historical data are available
• Future volatility may differ
from past
• Conceptual tool only
• Not empirically verified
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https://www.youtube.com/watch?v=8w43SUAZsY0
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